In places that don't have the 3rd restroom, it's entirely acceptable and appropriate for fathers to take their young daughters with them into the men's room. I cannot count the number of times mine has come in with me and she has excellent manners and knows not to stare.
My daughter is 4 and although I let her go into the women's room alone while I wait outside for her, when I have to use the restroom, she comes in with me.
NO WAY IN HELL would I even think of leaving her outside alone to wait for me, nor would I go into the men's room while she was in the women's room.
In places that have the 3rd restroom, yes, the father should take his daughter in there with him.
As for the cut-off age, honestly, I would say age 8, and certainly no younger than 7, but I won't be able to say for sure until mine reaches that age. She turns 5 this summer and she's not even close to being old enough for me to think of leaving her alone in a public place even for 30 seconds.
I live in southern California and people steal little girls here. It won't happen to mine.